I would stay away from being a pathologist, who has to cut up dead human tissue, or a surgeon (any type), who has to cut up live human tissue. Obstetricians, who deliver babies, get lots of fluids (pee, poop, blood, and amniotic fluid on them). Some people don't like feet, and so they shouldn't be podiatrists, and gynecologists and proctologists have to deal with genitalia, which is not for squeamish people.
If you don't want to be a doctor, then you could be anything on the administrative side, like a receptionist, coder, or biller, and if you don't mind needles, then you could be a lab technician, although you would have to deal with other bodily fluids.
Keep in mind that a lot of people start off medical school being squeamish, and a lot of people even faint the first time they do something, but most people get used to it with time and exposure, and you might find that you're less squeamish than you think.